Aggregation error bounds for a class of location models

Operations Research

Volumn 48, Issue 2, 2000, Pages 294-307

  Francis, R L ^a   Lowe, T J ^b   Tamir, Arie ^c  

^a University of Florida   (United States)

^b UNIVERSITY OF IOWA   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; ERROR ANALYSIS; HEURISTIC METHODS; LOCATION;

AGGREGATION ERROR BOUNDS; DEMAND POINT AGGREGATION; LOCATION MODELS;

OPTIMIZATION;

EID: 0034156131     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.48.2.294.12382     Document Type: Article

References (56)

1. Andersson, G., R. L. Francis, T. Nonnark, M. B. Rayco. 1998. "Aggregation method experimentation for large-scale network location problems," Location Sci., 6 25-39.
2. Andreatta, G., F. M. Mason. 1985a. K-eccentricity and absolute k-centrum of a probabilistic: tree. European J. Oper. Res. 19 114-117.
3. _, _. 1985b. Properties of the k-centra in a tree network. Networks 15 21-25.
4. Berman, O., D. Simchi-Levi. 1990. Conditional location problems on networks. Transp. Sci. 24 77-78.
5. _, J. Hodgson, D. Krass. 1995. Flow interception problems. Chapter 17 in Facility Location: a Survey of Applications and Methods. Z. Drezner (ed.). Springer Verlag, New York, 389-426.
6. Burkard, R. 1990. Locations with spatial interactions: the quadratic problem. Chapter 9 in Discrete Location Theory. P. B. Mirchandani and R. L. Francis (eds.). J. Wiley & Sons, New York, 387-438.
7. Casillas, P. A. 1987. Data aggregation and the p-median problem in continuous space. In Spatial Analysis and Location Allocation Models, A. Ghosh and G. Rushton (eds.), Van Nostrand Reinhold Publishers, New York, 227-244.
8. Chvatal, V. 1979. A greedy heuristic for the set covering problem. Math. Oper. Res. 4 233-235.
9. Current, J. R., D. A. Schilling. 1987. Elimination of source A and B errors in p-median location problems. Geographical Analysis 19 95-110.
10. _, _. 1990. Analysis of errors due to demand data aggregation in the set covering and maximal covering location problems. Geographical Analysis 22 116-126.
11. Daskin, M. S., A. E. Haghani, M. Khanal, C. Malandraki. 1989. Aggregation effects in maximum covering models. Ann. Oper. Res. 18 115-140.
12. Domich, P. D., K. L. Hoffman, R. H. F. Jackson, M. A. McClain. 1991. Locating tax facilities: a graphics-based microcomputer optimization model. Management Sci. 37 960-979.
13. Drezner, Z. 1989. On the conditional p-center problem. Transp. Sci. 23 51-53.
14. _. 1995. On the conditional p-median problem. Comput. Oper. Res. 22 525-530.
15. Elzinga, J., D. W. Hearn. 1972. Geometrical solutions for some minimax location problems. Transp. Sci. 6 379-394.
16. Erkut, E., B. Bozkaya. 1999. Analysis of aggregation errors for the p-median problem. Computers and Operations Research (Special Issue on Aggregation & Disaggregation for Operations Research) 26 1075-1096.
17. _, S. Neuman. 1989. Analytical models for locating undesirable facilities. European J. Oper. Res. 40 275-291.
18. Francis, R. L., T. J. Lowe. 1992. On worst-case aggregation analysis for network location problems. Ann. Oper. Res. 40 229-246.
19. _, _, M. B. Rayco. 1996. Row-column aggregation for rectilinear distance p-median problems. Transp. Sci. 30 160-174.
20. _, _, G. Rushton, M. B. Rayco. 1999. "A synthesis of aggregation methods for multi-facility location problems: strategies for containing error," Geographical Anal., 31 67-87.
21. _, L. F. McGinnis, J. A. White. 1992. Facility Layout and Location: an Analytical Approach. Prentice-Hall, Inc., Englewood Cliffs, NJ.
22. Geoffrion, A. 1977. Objective function approximations in mathematical programming. Mathematical Programming 13 23-37.
23. Goldberg, R. R. 1976. Methods of Real Analysis. Second Edition, J. Wiley and Sons, Inc., New York.
24. Goldman, A. J. 1971. Optimum location for centers in a network. Transp. Sci. 5 212-221.
25. Goodchild, M. F. 1979. The aggregation problem in location-allocation. Geographical Analysis 11 240-254.
26. Halpern, J. 1978. Finding minimal center-median convex combination (cent-dian) of a graph. Management Sci. 24 535-544.
27. Hakimi, S. L. 1964. Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12 450-459.
28. _. 1965. Optimum distribution of switching centers in a communications network and some related graph-theoretic problems. Oper. Res. 13 462-475.
29. _, E. F. Schmeichel, M. Labbé. 1993. On locating path-or tree-shaped facilities on networks. Networks 23 543-555.
30. Handler, G. Y. 1985. Medi-centers of a tree. Transp. Sci. 19 246-260.
31. _, P. B. Mirchandani. 1979. Location on Networks: Theory and Algorithms, The MIT Press, Cambridge, MA.
32. Hillsman, E. L., R. Rhoda. 1978. Errors in measuring distances from populations to service centres. Ann. Regional Sci. 12 74-88.
33. Hochbaum, D. S., W. Maas. 1985. Approximation schemes for covering and packing problems in image processing and VLSI. JACM 32 130-136.
34. Hodgson, M. J., S. Neuman. 1993. A GIS approach to eliminating source C aggregation error in p-median models. Location Sci. 1 155-170.
35. Hooker, J. N., R. S. Garfinkel, C. K. Chen. 1991. Finite dominating sets for network location problems. Oper. Res. 39 100-118.
36. Iyer, A. V., H. D. Ratliff. 1990. Accumulation point location on tree networks for guaranteed time distribution. Management Sci. 36 958-969.
37. Kumar, A., L. Schwartz, J. Ward. 1995. Risk-pooling along a fixed delivery route using a dynamic inventory-allocation policy. Management Sci. 41 344-362.
38. Lee, H., C. Billington, B. Carter. 1993. Hewlett-Packard gains control of inventory and services through design for localization. Interfaces 23 1-11.
39. Lin, J.-H., J. S. Vitter. 1992. Approximation algorithms for geometric median problems. Information Processing Letters 44 245-249.
40. Minieka, E. 1980. Conditional centers and medians on a graph. Networks 10 262-272.
41. Mirchandani, P. B., A. R. Odoni. 1979. Locating new passenger facilities on a transportation network. Transp. Res. 13B 113-122.
42. _, R. L. Francis (ed.). 1990. Discrete Location Theory. J. Wiley & Sons, New York.
43. _, J. M. Reilly. 1986. Spatial nodes in discrete location problems. Ann. Oper. Res. 10 329-350.
44. Murray, A. T., J. M. Gottsegen. 1997. The influence of data aggregation on the stability of p-median location model solutions. Geographical Analysis 29 200-213.
45. Pardalos, P. M., H. Wolkowicz (eds.). 1994. Quadratic Assignment and Related Problems. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 16, American Mathematical Society: Chapter 1, "The Quadratic Assignment Problem," pp. 1-42.
46. Plastria, F. 1996. How to choose aggregation points for continuous p-median problems: a case for the gravity centre. Report BEIF/88. Vrije Universiteit Brussel, Belgium.
47. Rayco, M. B., R. L. Francis. 1996. Asymptotically optimal aggregation for some unweighted p-center problems with rectilinear distances. Studies in Locational Analysis 10 25-36.
48. _, _, T. J. Lowe. 1997. Error-bound driven demand point aggregation for the rectilinear distance p-center model. Location Sci. 4 213-235.
49. Rockafellar, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
50. Rosenbaum, R. A. 1950. Sub-additive functions. Duke Math. J. 17 227-247.
51. Rushton, G. 1989. Applications of location models. Ann. Oper. Res. 18 25-42.
52. Shier, D. R., P. M. Bearing. 1983. Optimal locations for a class of nonlinear, single-facility location problems on a network. Oper. Res. 31 292-303.
53. Slater, P. J. 1978. Centers to centroids in a graph. J. Graph Theory 2 209-222.
54. Tamir, A., T. J. Lowe. 1992. The generalized p-forest problem on a tree network. Networks 22 217-230.
55. Williams, J. C., Jr. 1995. Political redistricting: a review. Papers in Regional Sci. 74 13-40.
56. Zemel, E. 1985. Probabilistic analysis of geometric location problems. SIAM J. Alg. Disc. Meth. 6 189-200.